Read the two sentences below and choose the transition that best fills in the blank: the day started out cold and rainy. we arrived at the mall soggy and chilly. as a result for example however regardless

It wouldn't make sense to make an example on how it is cold and rainy.
Also to say 'however' would require to follow by something opposite to the previous sentence/clause.
To say 'regardless' would indicate whether it was rainy or not, you would end up at the mall soggy and chilly.
So it makes more sense to use 'As a result.'

As a result we arrived at the mall soggy and chilly